Eigenvalue Placement Approach to Synchronization of Networked Nonlinear Oscillators

This paper is concerned with synchronization of nonlinear oscillators coupled via a directed network. It is known that that the synchronization can be achieved by choosing the coupling weights such that nonzero eigenvalues of the weighted Laplacian are located inside a certain convex region. We present a design method of the coupling weights which achieves the desired eigenvalue placement based on the bilinear matrix inequality optimization. The present method improves the previously reported method by the authors (Hibi and Takaba (2012)) by introducing a more general convex region for the eigenvalue placement.